Question

Bài 1:

a. \(\left(5^{2010}+5^{2012}+5^{2014}\right):\left(5^{2011}+5^{2009}+5^{2007}\right)\)

b. \(\left(-\dfrac{7}{45}\right)-\left(-\dfrac{1}{4}\right)-\left(-\dfrac{3}{5}\right)+\dfrac{1}{12}+\dfrac{2}{3}+\dfrac{1}{39}-\left(-\dfrac{5}{9}\right)\)

Answer 1

\(a)\left(5^{2010}+5^{2012}+5^{2014}\right):\left(5^{2011}+5^{2009}+5^{2007}\right)\)

\(=\dfrac{5^{2007}\left(5^3+5^5+5^7\right)}{5^{2007}\left(5^4+5^2+1\right)}=\dfrac{5^3+5^5+5^7}{5^4+5^2+1}\)

\(=\dfrac{125+3125+78125}{625+25+1}=\dfrac{81375}{651}=125\)

\(b)-\dfrac{7}{45}+\dfrac{1}{4}+\dfrac{3}{5}+\dfrac{1}{12}+\dfrac{2}{3}+\dfrac{1}{39}+\dfrac{5}{9}\)

\(=\dfrac{-7.52+1.585+3.468+1.195+2.780+1.60-5.260}{2340}\)

\(=\dfrac{-364+585+1404+195+1560+60-1300}{2340}\)

\(=\dfrac{2140}{2340}=\dfrac{107}{117}\)